If I remember right, Seeley gives an explicit example of sequences (a_n) and (b_n). Have you tried modifying them to get sequences that suffice for the general case?
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Loop SpaceSep 11 '12 at 11:35

(But Jochen's right: the easiest way is via the isomorphisms. Still, if you want to have an extension operator built in the same way as Seeley's then I suggest trying to modify Seeley's sequences.)
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Loop SpaceSep 11 '12 at 11:36